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Statistics 5 Mark Each

Board Question Paper : July 2019 · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 4 questions.

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4 questions · timed · auto-graded

Question 15 Marks
Find a linear equation using the method of least squares for the trend of production from the following data about sugar production of a country recorded for the last $6$ years. Find the trend estimates for the production of the year $2016-17$ and $2017-18$.
Year $2009-10$ $2010-11$ $2011-12$ $2012-13$ $2013-14$ $2014-15$
Production
$($Crore tons$)$		 $29.2$ $34.2$ $35.4$ $36.4$ $33.6$ $37.7$
OR
The data about closing prices of shares of a company registered in a stock exchange for different months is given in the following table. Find the trend using three monthly moving averages.
month Jan. Feb. Mar. April may June July Aug. Sept. Oct.
Share
Price ₹		 $176$ $173$ $165$ $168$ $167$ $160$ $163$ $167$ $165$ $166$
Answer
$39.78,40.97$ crore tons. OR $171.33 ; 168.07 ; 166.07;165;$ June $163.33;$ July $163.33;$ August $165$; Stp $165.$
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Question 25 Marks
The following information is obtained from a study to know the effect of use of fertilizer on the yield of cotton :
Consumption of fertilizer $(10\ kg ) x$ $28$ $35$ $25$ $24$ $20$ $25$ $20$
Yield of cotton per hectare $($Quintals$) y$ $128$ $140$ $115$ $120$ $105$ $122$ $100$
Obtain the regression line of $Y$ on $X$ and estimate the yield of cotton per hectare if $300\ kg$ fertilizer is used.
Answer
$130.44$
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Question 35 Marks
From the following information of a sample of ten students of a school regarding their marks in two subjects Accountancy and Statistics, find the coefficient of correlation between the marks of two subjects
Marks in Accountantancy $60$ $80$ $50$ $80$ $95$ $40$ $70$ $40$ $35$ $90$
Marks in Statistics $50$ $75$ $60$ $85$ $90$ $40$ $65$ $30$ $465$ $70$
Answer
$0.9$
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Question 45 Marks
The quantity consumed and total expenditure of four different items are as given below. Find Laspeyre's, Paasche's and Fisher's index numbers for the year $2017$ with respect to the year $2015 :$
Item Year $2015$ Year $2017$
Total
Expenditure
(₹)		 Consumption
(Quantity)		 Total
Expenditure
(₹)		 Consumption
(Quantity)
$A$ $360$ $60 \ kg$ $375$ $25 \ kg.$
$B$ $160$ $10$ litre $416$ $20$ litre
$C$ $480$ $15 \ kg.$ $613.2$ $6 \ kg.$
$D$ $336$ $3 \ kg.$ $400$ $2.5 \ kg.$
Answer
$I_L=233.61, I_P=191.53, I_F=211.53$
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5 Mark Each - Statistics STD 12 Commerce Questions - Vidyadip